NUMERICAL SIMULATIONS AND ANALYSIS OF THE THERMAL EFFECTS ON SILICON CARBIDE DURING DUCTILE MODE MICRO-LASER ASSISTED MACHINING

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1 Proceedings of the ASME 29 International Manufacturing Science and Engineering Conference MSEC29 October 4-7, 29, West Lafayette, Indiana, USA MSEC NUMERICAL SIMULATIONS AND ANALYSIS OF THE THERMAL EFFECTS ON SILICON CARBIDE DURING DUCTILE MODE MICRO-LASER ASSISTED MACHINING Saurabh R. Virkar # Industrial and Manufacturing Engineering Western Michigan University Kalamazoo, MI-498, USA. John A. Patten* Manufacturing Engineering Western Michigan University Kalamazoo, MI-498, USA. ABSTRACT Various 2-D numerical simulations were carried out using the commercial software AdvantEdge Versions 5.2 and 5.3 to model ductile mode micro-laser Assisted Machining (µ-lam) of Silicon Carbide (4H-SiC). The cutting tool is a single oint diamond. The workiece material (SiC) is heated locally by a laser beam, which asses through the diamond tool ti. The workiece is heated beyond the thermal softening oint in order to study the effect of increased temerature. The cutting and thrust forces are reduced when machining is done above the thermal softening temerature. The simulations were carried out for two cases at different temeratures above and below the thermal softening oint to study the effect of µ-lam on the cutting and thrust forces. In the first case both the tool and workiece material were heated to study the behavior at elevated temeratures. In the second case, a thermal boundary condition was rovided on the to surface of the workiece to simulate the laser heating effect keeing the tool at room temerature (2⁰ C). In both cases the chi formation was observed and the changes in cutting and thrust forces were evaluated. The simulation results indicate a significant decrease in machining forces if Silicon Carbide is heated beyond the thermal softening temerature thus demonstrating the benefits of µ-lam rocess. Keywords: Precision machining, Single Point Diamond Turning, Thermal softening, 4H Silicon Carbide 1 INTRODUCTION Silicon Carbide (SiC) is an advanced engineered ceramic and an alternative to semiconducting Silicon (Si) for oeration at elevated temeratures and high ower alications. Some of SiC s beneficial roerties include: chemical resistance, high temerature resistance, extreme hardness and high stiffness [1]. Also Silicon carbide is one of the non oxide ceramics that are found in various commercial alications and hence it has a good corrosion and erosion resistance [2]. SiC has a relatively high hardness, ~ 26 GPa and is nominally a brittle material [13]. Hence machining of SiC is difficult as the cutting damage (fracture) into the workiece. The classic roerty and benefit of SiC is that it retains its strength even at elevated temeratures, which imoses additional challenges for laser assisted (elevated temerature) machining. Current limitations for brittle material machining include the high cost of rocessing and roduct reliability. The cost is mainly due to the high tool cost, raid tool wear, long machining time, low roduction rate and the manufacturing of satisfactory surface figure and form. The low roduct reliability is rimarily due to the occurrence of surface/subsurface damage and brittle fracture. Laser Assisted Machining (LAM) is a romising way of lowering the material strength during machining [5]. LAM can also increase the material removal rates while maintaining the workiece surface quality. In LAM rocesses, the workiece is heated locally by a laser, ast its thermal softening oint, and then ductile mode machining is done on the thermally softened surfaced [5]. In µ-lam, the laser beam asses through the diamond tool, thus heating the surface just below the tool ti in the chi formation zone [2]. The heating effect roduced is at the microscoic scale and hence the laser ower required to heat the workiece is less than in macro LAM rocesses [8]. During LAM rocessing the workiece is deformed below the fracture strength, thereby enabling a visco-lastic flow rather than brittle fracture [5]. The workiece used in this study is crystalline 4H-SiC. This simulation work was done obtain the behavior of single crystal SiC at elevated temeratures to erform ductile mode machining. The objective of this study is to simulate the change in the chi formation and study the resultant machining forces with and without laser heating. The workiece is heated above the thermal softening oint to analyze the change in cutting and thrust forces during machining. The cutting ressure also decreases as the workiece temerature increases by the laser heating effect. As these ceramic materials are exensive, simulations rove to be a suitable tool to comlement the hysical exeriments. The simulations also rovide sufficient data to relate to the exeriment results. forces may be very high, which can damage the tool as well as imart # saurabh.r.virkar@wmich.edu *john.atten@wmich.edu 1 Coyright 29 by ASME

2 2 MATHEMATICAL MODEL 2.1 Introduction As the workiece is heated locally there is thermal softening and subsequent ductile material removal during machining. There is also a High Pressure Phase Transformation (HPPT) at the tool-chi interface, and the resultant hase obtained is ductile (metallic or amorhous) in certain ceramics such as Silicon Nitride and SiC [4]. The ductile material removal below the thermal softening oint is due to HPPT. The existence of high ressure hase beyond the thermal softening oint is not yet reorted. By confining the scoe of the simulation to the ductile mode of material removal, it is ossible to use the metal machining simulation software AdvantEdge to redict the behavior of SiC. The software currently only includes ductile or lastic deformation and does not consider a fracture criterion or brittle material removal mechanisms. In the ductile mode (even for ceramics), the software can be used to accurately redict the forces and ressures generated by the tool-workiece interaction, for a given set of rocess conditions assuming an aroriate material model is used [7]. Material roerties are secified in the model which includes elastic and lastic behavior, heat transfer, thermal softening as well as strain rate sensitivity. The simulation (material model) uses the Drucker-Prager model to accommodate the ressure induced hase transformation and the resultant lastic/ductile behavior [7] Elastic Plastic Behavior The elastic behavior is secified by roviding the Elastic (Young s) modulus and Poisson s ratio. The strain hardening behavior for the Drucker-Prager model is defined as g ε = σ Θ T 1 + ε ε where is the initial yield stress, is the lastic strain, is the reference lastic strain, Θ T is the thermal softening function and n is the strain hardening exonent. The initial yield stress is calculated using the Drucker-Prager yield criterion [7]. 1 n Thermal Softening Behavior The thermal softening function Θ (T) is defined as (1) limitation of the simulation software and was used to study the thermal effects on SiC above the thermal softening temerature Note: The temerature values T cutoff and T melt are estimated based on different values from various references [8-16] Strain Rate Sensitivity The strain rate sensitivity is given by 1 + ε ε Thermal Softening Curve for 4H SiC 1 + ε ε = 1 + ε t ε m σ 1 g(ε, if ε ) ε t m 2 m 1 = T cutoff T melt Figure 1 Thermal Softening Curve for 4H-SiC Thermal Softening Curve for 4H SiC m σ 2 g(ε, if ε ) > ε t where σ is the effective von Mises stress, g is the flow stress, ε is the accumulated lastic strain rate, ε is the reference lastic strain rate, and m 1 and m 2 are low and high strain rate sensitivity exonents, resectively. ε t is the threshold strain rate which searates the two regimes. The ertinent workiece material roerties are given in Table 1. The strain rate sensitivity (refer to Figure 2) is normalized to the initial yield stress [7]. (4) (5) Table 1 Workiece material roerties (Ref. [8]) The olynomial coefficients c through c 5 are fit to a 5 th order olynomial, T is the temerature, T cut is the linear cutoff temerature and T melt is the melting temerature. For the olynomial shown in equation (2), c is set to 1 while c 1 through c 5 are set to zero in the AdvantEdge software. Thus the value of thermal softening is 1 for temeratures below or equal to the cutoff temerature of the material, reaching a value of zero at the melting temerature as seen in figure 1. This simle model is a current (2) (3) Material roerties Value Units Elastic Modulus, E 33 GPa Poisson s ratio Hardness, H 26 GPa Initial yield stress, σ GPa Reference lastic strain, ε σ /E - Accumulated lastic strain, ε 1 - Strain hardening exonent, n 5 - Low strain rate sensitivity 1 - exonent, m 1 High strain rate sensitivity 1 - exonent, m 2 Threshold strain rate, ε t 1E7 sec -1 2 Coyright 29 by ASME

3 Flow stress Strain Rate Sensitivity Strain Rate (1/sec) Figure 2 Strain rate sensitivity normalized to initial yield stress 2.2 Determination of Initial Yield Stress To determine the initial yield stress, a ressure sensitive Drucker-Prager model as roosed by Ajjarau et al. (24) was secified as detailed below. The Drucker-Prager yield criterion is given by Flow stress = (5) incororate crystallograhic lanes/orientations and treats the material as elastic-lastic and ductile. To reflect the ductile behavior in ceramics, romoted by the HPPT, a ressure sensitive Drucker-Prager constitutive model as exlained in section 2.2 is used. The objective of these simulations was to study ductile machining behavior of single crystal SiC above its thermal softening temerature. For this study, the crystalline deendency of the brittle behavior of SiC is not included in the model, as the rimary goal is to study the thermal softening and resultant lastic and ductile material resonse. The simulations were carried out in two stages. In the first stage both the tool and workiece were heated and, in the second stage a thermal boundary condition was rovided on the to surface of the workiece to simulate the laser heating effect. (Note: The simulation software does not rovide for the direct incororation of the laser heat source, thus the heating effect is modeled with these thermal conditions) The simulation inut consists of the workiece and tool dimensions and their mechanical and thermal roerties as described in the next section. The tool and workiece material models used in this simulation work are similar to comarison study between numerical simulations and single oint diamond turning exeriments done by Patten et al. (28), which demonstrates that the material models are quite reliable [1,2]. 3.1 Workiece model and Proerties J 2 is the second invariant of the deviatoric stress tensor, given by J 2= 1 [ σ1- σ2 ²+ σ2- σ3 ²+ σ3- σ1)²] (6) 6 I 1 (I 1 =σ 1 + σ 2 + σ 3 ) is the first invariant of stress tensor, α is the ressure sensitivity coefficient, κ is the initial yield stress. The quantity κ is given by κ = 2 σ t σ c σ t +σ c (7) where σ t and σ c are the yield strength in tension and comression, resectively. The quantity κ is equal to the flow stress in the case when σ c = σ t, i.e. no ressure deendency. The hardness of SiC material is taken as 26 GPa [9, 15] and the tensile yield stress is calculated to be GPa based on a roosed value of H/2.2 [18]. The comressive yield (σ c ) is set to equal the hardness of the material [8]. For a uniaxial stress state (σ 2 and σ 3 are zero), From equation (8) we get, I 1 = σ 1 (8) J 2 = σ From equation (9), κ equals GPa and from equation (5), α equals.375. These two arameters are set in the software material model to rovide a ressure sensitive (Drucker-Prager) yield criterion. 3. SIMULATION MODEL The simulation method is based uon a 2-D Lagrangian finiteelement machining model assuming lane strain conditions [19]. The simulations were carried out by secifying the material roerties for olycrystalline α-4h-sic. Thus, the constitutive model does not (9) Figure 3 Simulation Model The workiece was made long enough (L =.8 mm) to ensure that the length of cut (loc) would allow steady state conditions to be achieved. The height (h =.2 mm) of the workiece was much larger (between 1 to 1 times) in comarison to the feed (f) or uncut chi thickness (t). The boundary conditions of the workiece surface is assumed to be traction free and constrained in vertical direction. Refer to Figure 3 and 4 for these dimensions. The thermal roerties of the SiC are given in Table 2. Table 2 Thermal roerties of workiece (SiC) (Ref. [8]) Proerties Value Thermal Conductivity (W/m ⁰ C) 39 *Thermal Softening temerature (⁰ C) 2 *Melting temerature (⁰ C) 32 Initial reference temerature (⁰ C) 2 * Note: The thermal softening and melting temerature of SiC given in table 2 are estimated based on various references [8-16] to study the behavior of SiC while machining above thermal softening temerature. 3.2 Tool Secifications The tool used is a single oint diamond. The tool arameters are given in table 3. The simulations were conducted in 2-D and as a result a round nose tool geometry could not be simulated, therefore the simulated tool cutting edge is flat. The to and rear surfaces of the tool are rigidly fixed with adiabatic conditions. The material model for the 3 Coyright 29 by ASME

4 tool is olycrystalline diamond with elastic roerties as given in Table 4. Table 3 Tool Parameters/Geometry Edge Radius, r, (nm) 1 Rake angle, α - 45º Relief angle, β 5º Rake length (mm).75 Relief length (mm).75 used for comarison to evaluate the various machining conditions (rimarily the workiece temerature and the resultant thermal softening effect). All simulated force results are based on achieving steady-state conditions. The initial temerature of the workiece and tool is set at room temerature (2⁰ C). To study the various effects of heating on SiC, two different conditions were used to study the behavior of SiC. In the first case, both the tool and workiece were heated. In the second case, a thermal boundary condition was rovided on the to surface of workiece to artificially increase the temerature in an effort to simulate the effect of the µ-lam rocess. The simulations were carried out at various temeratures above and below the thermal softening oint of SiC. The simulation temeratures were 2⁰ C, 1⁰ C, 19⁰ C, 2⁰ C, 23⁰ C, 26⁰ C and 31⁰ C, where 2º C is the thermal softening temerature as shown in figure 1. The feed and cutting edge radius were ket constant in all simulations. The results of the simulations were viewed in Teclot [7] which rovides temerature, ressure and stress contours along with the cutting and thrust force lots for analysis of the simulation results. At each of the simulated temeratures, the chi formation, force lots and ressure contours are used and comared to evaluate the results. 4 RESULTS In the first case when both the tool and workiece were heated to the same temerature, the comarisons of the different simulations are made with reference to the simulation at room temerature as shown in figure 5. Figure 4 Tool and Workiece geometry The -45⁰ rake angle creates a high ressure sufficient to accommodate the HPPT, thus the chi formation zone is conducive for ductile deformation [6]. The thermal and mechanical roerties of diamond are given in table 4. Table 4 Tool Proerties (Ref. [8]) Thermal Conductivity, W/m ⁰C 15 Heat Caacity, J/kg ⁰C Density, kg/m³ 352 Elastic Modulus, GPa 15 Poisson's ratio.2 Figure 5 (At 2⁰ C) 3.3 Simulation Process Process arameters used in the simulations are given in table 5. Table 5 Process Parameters Parameters Values Feed (nm) 5 Coefficient of friction.5 seed (m/s) 1 Deth of cut (mm).2 The simulations were conducted with the values given in Tables 2, 3, 4 and 5. The feed in the 2-D simulation relates to the uncut chi thickness, and the deth of cut refers to the workiece width. With the given values of high negative rake angle and feed, ductile mode machining was achieved in the exeriments erformed by Patten et al. (25). The coefficient of friction was taken as.5 however the results are not very sensitive to this value as established in revious research [8]. The simulation results include the cutting and thrust forces that are Figure 6 (At 1⁰ C) 4 Coyright 29 by ASME

5 Forces Figure 7 (At 19⁰ C) Figure 11 (At 31⁰ C) From figures 5-8 it can be seen that from 2 ⁰C until the thermal softening temerature of 2 ⁰C there is no significant change in the chi formation. Note that the temerature scale changes in each figure, as the minimum temerature is set to the re-heating temerature. The workiece undergoes lastic deformation and high ressures are observed at the tool-workiece interface. Figures 9, 1 and 11 deict the thermal softening behavior as the chi thickness increases due to decrease in the hardness of SiC. The lower cutting forces enhance recision machining through increased ductile material removal. The simulation results are summarized in Table 6 Figure 8 (At 2⁰ C) Temerature of simulation (ºC) Table 6 Simulation results Maximum Pressure (GPa) force Thrust force Figure 9 (At 23 ⁰C) Forces vs. Temerature Plot Force Thrust Force Temerature (⁰ C) Figure 1 (At 26⁰ C) Figure 12 5 Coyright 29 by ASME

6 Pressure (GPa) Pressure (GPa) Pressure (GPa) Figure 15 (1⁰ C boundary condition on workiece) Temerature (⁰ C) Figure 13 From table 6 and figure 12, it can be seen that there is a sudden change in cutting and thrust forces at temeratures above the thermal softening temerature (2⁰ C). The change in cutting ressure (refer to Figure 13) is due to a decrease in hardness of SiC above the thermal softening oint. To generate a ductile cutting environment through urely alied stress (hydrostatic and shear) required that the ressures at the tool-chi interface be equal to or higher than, the hardness of the material [21], which is taken to be 26 GPa in the material model. In the simulation at 31 ⁰C the forces and ressure are negligible as the workiece material is close to the melting temerature (32 ⁰C). The chi formation is ductile at all temeratures and above the thermal softening temerature, the chi thickness increases. In the second set of simulations, a thermal boundary condition was rovided on the to surface of the workiece (refer to Figure 14) keeing the tool at room temerature (2º C). These simulations were done to simulate laser assisted machining such that the workiece is heated by the laser before machining. Note that the temerature scale changes in each figure (Figures 15-2), as the minimum temerature is set at 1º C less than the boundary condition temerature to show the effect of thermal boundary condition on the to surface of the workiece. The figures 15-2 deict the second stage simulation results. Figure 16 (19⁰ C boundary condition on workiece) Figure 17 (2⁰ C boundary condition on workiece) Figure 14 (Workiece Boundary Condition) Figure 18 (23⁰ C boundary condition on workiece) 6 Coyright 29 by ASME

7 Forces Forces Pressure (GPa) Pressure (GPa) Figure 19 (26⁰ C boundary condition on workiece) Temerature (⁰C) Figure 22 Pressure Plot Figure 2 (31⁰ C boundary condition on workiece) In these simulations the thermal boundary condition temerature on the workiece was varied from 1⁰ C to 31⁰ C. In these simulations the tool is also heated (via conduction) aroaching the workiece temerature. As diamond is a good conductor of heat, heat transfer readily takes lace from the workiece to the tool. Table 7 Results of workiece boundary condition simulation Temerature of simulation(ºc) Maximum Pressure (GPa) force Thrust force Forces vs. Temerature Plot Figure Temerature (⁰C).16 Force Thrust Force From figure 21, it can be seen that there is a change in cutting and thrust forces above the thermal softening temerature. Theoretically, below the thermal softening temerature (2⁰ C), the cutting and thrust forces should be aroximately remain the same. But in the boundary condition simulations, the cutting and thrust force values also vary slightly due to variation in mesh arameters used in the software. But the behavior of SiC is the same in both cases. The cutting ressure remains high until the thermal softening oint (2⁰ C) as SiC retains its strength and hardness u to the thermal softening oint. Above the thermal softening oint the strength begins to decrease gradually (as indicated in figure 1) and so do the machining forces. As the temerature aroaches the melting temerature (32⁰ C) the workiece starts iling u on the rake face of the tool. This henomena is due to a decrease in hardness and enhanced ductility at elevated temerature [8, 11] 5 Conclusions From the summary of data in tables 6 and 7 it can be seen that there is considerable change in cutting and thrust forces. Tables 8 and 9 indicate the ercentage decrease in forces (cutting and thrust resectively) by comaring the simulations at 26º C to those at 2º C i.e. above and at the thermal softening temerature. Table 8 Change in Forces Both tool and workiece heated (Case 1) Boundary condition on workiece (Case 2) Table 9 Change in Thrust Forces Both tool and workiece heated (Case 1) Boundary condition on workiece (Case 2) Percentage 24% 26% Percentage 28% 31% The dro in cutting and thrust forces when the workiece is heated above the thermal softening temerature (2 ⁰C) was significant (24% to 31%) as calculated by considering the values of the cutting and thrust forces at 2 ⁰C and 26 ⁰C, as shown in tables 9 and 1. 7 Coyright 29 by ASME

8 Below 2⁰ C the cutting and thrust forces remain almost constant as there is no thermal softening. The chi formation is also seen to change above the thermal softening temerature; above this temerature, the chi formation is quite ductile and hence the chi thickness also increases. 6 FUTURE WORK Current ongoing work includes a thermal boundary condition only on the tool ti. Also 3D scratch test simulations are being conducted to comare with exeriments [22]. The scratch tests simulations are being done at various feeds/deths at which the exeriments were erformed. 7 ACKNOWLEDGEMENTS The authors would like to thank ThirdWave Systems Inc., for their generous suort and technical assistance. The authors are also thankful to the National Science Foundation (NSF) for their grant CMMI REFERENCES [1] Osiander, R., Chamion, J., Darrin, M., 26, MEMS and Microstructures in Aerosace Alications, CRC Press, Boca Raton, Florida, US,. 321 [2] Srinivasan, M., Ranfaniello, W., 1997, Acheson Process. Carbide, Nitride and Boride Materials Synthesis and Processing, Weimer, A. W., Ed., Chaman and Hall, London, United Kingdom, [3] Patten, J., Cherukuri, H., Yan, J., 24, Ductile Regime Machining of Semiconductors and Ceramics, Inst. of Physics Publishing,. 616 [4] Patten, J., Bhatt, B., 26, Single Point Diamond Turning of CVD coated Silicon Carbide, ASME J. of Manufacturing Science and Engineering, Vol. 127,. 522 [5] Shin, Y., C., Pfefferkorn, F., E., Rozzi, J., C.,2, Exerimental Evaluation of the Laser Assisted Machining of Silicon Nitride Ceramics ASME, J. of Manufacturing Science, 2, Vol. 122,. 666 [6] Patten, J., A., Gao, W., Yasuto, K., 25, Ductile Regime Nanomachining of Single Crystal Silicon Carbide, ASME Journal of Manufacturing Science and Engineering, 127 (8), [7] Advantedge User Manual, Version 5.3, 29 [11] Shim, S., Jang, J-I., Pharr, G., M., 28, Extraction of flow roerties of Single Crystal Silicon Carbide by Nanoindentation and Finite Element Simulation, Act. Materia., 58, [12] Yonenaga, I., 21, Thermo-Mechanical Stability of Wide- Bandga Semiconductors:High Temerature Hardness of SiC, AlN, GaN, ZnO and ZnSe, Physica B. (38-31), [13] Yonenaga, I., Hoshi, T., Usui, A., 2, High Temerature Strength of III-IV Nitride Crystals, J. Phys: Condens. Matter, 14, [14] Samant, A., V., Zhou, W., L., Pirouz, P., 1998, Effect of Test Temerature and Strain Rate on the Yield Stress of Monocrystalline 6H-SiC, Phys. Stat. Sol. (a) 166,. 155 [15] Tsvetkov, V., F., Allen, S., T., Kong, H., S., Carter, C., H., 1996, Recent Progress in SiC Crystal Growth, Inst. of Phys. Serial No. 142,. 17 [16] CREE material data sheet [17] Naylor, M., G., S., Page, T., F., 1979, The Effect of Temerature and Load on the Indentation Hardness Behavior of Silicon Carbide Engineering Ceramics, Proc. on Intl. Conf on Erosion of Soil and Imact, [18] Gilman, J., J., 1975, Relationshi between Imact Yield Stress and Indentation Hardness, J. of Alied Physics, 46 (4), [19] Marusich, T., D., Askari, E., 21, Modeling Residual Stress and Workiece Quality in Machined Surfaces, [2] Patten, J., A., Jacob, J., Bhattacharya, B., Grevstad, A., 27, Comarison between numerical simulation and Exeriments for Single Point Diamond Turning of Silicon Carbide, Society of Manufacturing Engineers, NAMRC Conf.,. 2 [21] O Connor, B., Marsh, E., Couey, J., 25, On the Effect of Crystallograhic orientations for Ductile Material Removal in Silicon Precision Engineering, Vol. 29 (1), [22] Shayan, A., Poyraz, B., Patten, J., 29, Force Analysis, Mechanical Energy and Laser Heating Evaluation of Scratch Tests on Silicon Carbide (4H-SiC) in Micro-Laser Assisted Machining (µ-lam) Process, ASME Manufacturing Science Conference, West Lafayette, Purdue University, submitted [8] Jacob, J., 26, Numerical Simulation on Machining of Silicon Carbide, Master s Thesis, Western Michigan University, MI [9] Ajjarau S. K., Cherukuri, H., Patten, J., Brand, C. J., 24, Numerical Simulations of Ductile Regime Machining of Silicon Nitride using Drucker Prager model, Proc. Inst. Mech. Engrs., 218 (C),. 1-6 [1] Patten, J., Jacob, J., 28, Comarison Between Numerical Simulations and Exeriments for Single Point Diamond Turning of Single Crystal Silicon Carbide, J. Manufacturing Processes, Vol. 1, Coyright 29 by ASME